# Bayesian Nonparametric Adaptive Spectral Density Estimation for Financial Time Series

## TL;DR

This paper introduces a Bayesian nonparametric method for adaptive spectral density estimation in financial time series, effectively distinguishing non-stationarity from long-range dependency.

## Contribution

It develops a novel Bayesian framework with reversible jump MCMC for jointly modeling non-stationarity and dependency in financial data, allowing non-parametric spectral estimation.

## Key findings

- Method performs well across various simulated data.
- Real data analysis shows presence of long-range dependency and non-stationarity.
- Provides a new approach for analyzing complex financial time series.

## Abstract

Discrimination between non-stationarity and long-range dependency is a difficult and long-standing issue in modelling financial time series. This paper uses an adaptive spectral technique which jointly models the non-stationarity and dependency of financial time series in a non-parametric fashion assuming that the time series consists of a finite, but unknown number, of locally stationary processes, the locations of which are also unknown. The model allows a non-parametric estimate of the dependency structure by modelling the auto-covariance function in the spectral domain. All our estimates are made within a Bayesian framework where we use aReversible Jump Markov Chain Monte Carlo algorithm for inference. We study the frequentist properties of our estimates via a simulation study, and present a novel way of generating time series data from a nonparametric spectrum. Results indicate that our techniques perform well across a range of data generating processes. We apply our method to a number of real examples and our results indicate that several financial time series exhibit both long-range dependency and non-stationarity.